Oscillatory results for second-order noncanonical delay differential equations

Abstract

The main purpose of this paper is to improve recent oscillation results for the second-order half-linear delay differential equation $\left(r(t)\left(y'(t)\right)^\gamma\right)'+q(t)y^\gamma(\tau(t))= 0, \quad t\geq t_0,$ under the condition $\int_{t_0}^{\infty}\frac{\text{d} t}{r^{1/\gamma}(t)} \lt \infty.$ Our approach is essentially based on establishing sharper estimates for positive solutions of the studied equation than those used in known works. Two examples illustrating the results are given.